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arXiv:quant-ph/9912104 · Physical Review Letters

Automatic Quantum Error Correction

Jeff P. Barnes, Warren S. Warren

Published Jul 24, 2000• 30 citations
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Abstract

Criteria are given by which dissipative evolution in the weak coupling limit can transfer populations and coherences between quantum subspaces, without a loss of coherence. The result is a form of quantum error correction implemented by the joint evolution of a system with a cold bath. It requires no external intervention and, in principle, no ancilla. An example of such a system, consisting of three dipole ordered spin 1/2 particles in a resonator, is given. The qubit, or the triple quantum coherence of the spins, is protected against all spin-flip errors.

DOI
10.1103/physrevlett.85.856

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Criteria are given by which dissipative evolution in the weak coupling limit can transfer populations and coherences between quantum subspaces, without a loss of coherence. The result is a form of quantum error correction implemented by the joint evolution of a system with a cold bath. It requires no external intervention and, in principle, no ancilla. An example of such a system, consisting of three dipole ordered spin 1/2 particles in a resonator, is given. The qubit, or the triple quantum coherence of the spins, is protected against all spin-flip errors.
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Abstract Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error-correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin-flips or phase-flips. Our dissipative error correction scheme operates in a continuous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.
We critically examine the internal consistency of a set of minimal assumptions entering the theory of fault-tolerant quantum error correction for Markovian noise. We point out that these assumptions may not be mutually consistent in light of rigorous formulations of the Markovian approximation. Namely, Markovian dynamics requires either the singular coupling limit (high temperature), or the weak coupling limit (weak system-bath interaction). The former is incompatible with the assumption of a constant and fresh supply of cold ancillas, while the latter is inconsistent with fast gates. We discuss ways to resolve these inconsistencies.
Physical qubits in a quantum computer are often represented by superposition states of single particles or excitations. Decay of the excitation itself is a fundamental error channel that is difficult to overcome via external drive or control techniques. Quantum error correcting codes, which encode information in superpositions involving multiple excitations, provide a path to preserve information beyond the capacity of individual excitations, but typically require exquisite active operations on the system. Here, we demonstrate a steady-state driven-dissipative quantum system, composed of a superconducting cavity and a transmon ancilla, that preserves a logical qubit beyond the photon-lifetime limit by about 5% using a binomial encoding. This realization of continuous quantum error correction at the breakeven point highlights the quantitative competitiveness of passive correction strategies, while circumventing some demanding hardware requirements of its active counterparts.
Control over spin dynamics has been obtained in NMR via coherent averaging, which is implemented through a sequence of RF pulses, and via quantum codes which can protect against incoherent evolution. Here, we discuss the design and implementation of quantum codes to protect against coherent evolution. A detailed example is given of a quantum code for protecting two data qubits from evolution under a weak coupling (Ising) term in the Hamiltonian, using an ``isolated'' ancilla which does not evolve on the experimental time scale. The code is realized in a three-spin system by liquid-state NMR spectroscopy on 13C-labelled alanine, and tested for two initial states. It is also shown that for coherent evolution and isolated ancillae, codes exist that do not require the ancillae to initially be in a (pseudo-)pure state. Finally, it is shown that even with non-isolated ancillae quantum codes exist which can protect against evolution under weak coupling. An example is presented for a six qubit code that protects two data spins to first order.